\subsection{可达速率域外界}\label{Cha:IC:SISO:OuterBound}
类似于可达速率内界的推导，第$ i $个传输对的可达速率$ R^{\mathrm{IC,SISO}}_i $上界为
\begin{subequations}\label{Eqn:IC:SISO:OuterBound:ABG}
    \begin{align}
    R^{\mathrm{IC,SISO}}_i &=\maximize{\left\{f_i\left(x_i\right)\right\}}{I\left(X_i;Y_i\right)}\\
    &=\maximize{\left\{f_i\left(x_i\right)\right\}}{h\left(Y_i\right)-h\left(Y_i\vert X_i\right)}\\
    &=\maximize{\left\{f_i\left(x_i\right)\right\}}{h\left(\sum_{j=1}^{K}g_{i,j}\left(X_j+b_j\right)+Z_i\right)-h\left(\sum_{j=1,j\neq i}^{K}g_{i,j}\left(X_j+b_j\right)+Z_i\right)}\\
    &\leq \frac{1}{2}\log_2 2\pi e \var{\sum_{j=1}^{K}g_{i,j}\left(X_j+b_j\right)+Z_i}\nonumber\\
    &\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad-\minimize{\left\{f_i\left(x_i\right)\right\}}{\frac{1}{2}\log_2\left(\sum_{j=1,j\neq i}^{K}2^{2 h\left(g_{i,j} X_j\right)}+2^{2 h\left(Z_i\right)}\right)}\label{Eqn:IC:SISO:OuterBound:d}\\
    &\leq\frac{1}{2}\log_2{\left(1+\frac{\sum_{j=1}^{K}g_{i,j}^2\varepsilon_j}{\sigma^2}\right)},\label{Eqn:IC:SISO:OuterBound:e}
    \end{align}
\end{subequations}
式中，不等式\eqref{Eqn:IC:SISO:OuterBound:d}是根据熵功率不等式，以及对于给定方差$ \var{Q} $的任意随机变量$ Q $，有$ h\left(Q\right)\leq \frac{1}{2}\log_2{2\pi e \var{Q}} $；不等式\eqref{Eqn:IC:SISO:InnerBound:e}是由于$ g_{i,j}^2 2^{2h\left(X_j\right)}\geq 0 $，去掉相应各项后化简得到。



因此，可见光干扰信道可达速率域的外界可以表示为
\begin{align}
\begin{cases}
R^{\mathrm{IC,SISO}}_1 &\leq \frac{1}{2}\log_2{\left(1+\frac{\sum_{j=1}^{K}g_{i,j}^2\varepsilon_j}{\sigma^2}\right)},\\
&\vdots\\
R^{\mathrm{IC,SISO}}_K &\leq\frac{1}{2}\log_2{\left(1+\frac{\sum_{j=1}^{K}g_{i,j}^2\varepsilon_j}{\sigma^2}\right)}.
\end{cases}
\end{align}